Analysis of patterns formed by two-component diffusion limited aggregation

We consider diffusion limited aggregation of particles of two different kinds. It is assumed that a particle of one kind may adhere only to another particle of the same kind. The particles aggregate on a linear substrate which consists of periodically or randomly placed particles of different kinds. We analyze the influence of initial patterns on the structure of growing clusters. It is shown that at small distances from the substrate, the cluster structures repeat initial patterns. However, starting from a critical distance the initial periodicity is abruptly lost, and the particle distribution tends to a random one. An approach describing the evolution of the number of branches is proposed. Our calculations show that the initial patter can be detected only at the distance which is not larger than approximately one and a half of the characteristic pattern size.Comment: Accepted for publication in Physical Review

The effects of various household cleaning methods on DNA persistence on mugs and knives

© 2019 Elsevier B.V. With the prevalence of forensic science in popular media, offenders are becoming more forensically aware and can employ precautionary methods, such as cleaning used items or rubbing away fingermarks, to reduce their traces left at a crime scene. This study examined the effects of various cleaning methods on DNA persistence on commonly encountered casework exhibits, specifically knives and mugs. Aliquots of acellular DNA were added to the knife handles or mug rims, allowed to dry, and then the substrates were either sampled directly or were cleaned and then sampled. The plastic- and wood-handled knives were cleaned with a cloth in a sink of water, diluted dish washing liquid or diluted household bleach, whereas the ceramic, glass and steel mugs were cleaned with a dry or wet cloth, or by wiping with a cloth after applying a cleaning product (dish washing liquid or household bleach spray) directly into the mug and then rinsing it with water. DNA samples were collected with wet and dry swabs, in triplicate, and extracted and quantified. In both experiments, DNA was not detected on items after cleaning with dish washing liquid or household bleach, irrespective of the differences in amounts of DNA initially deposited, substrates, and cleaning methods. Even without a cleaning product, rubbing with a dry cloth decreased DNA recovery from the mugs, regardless of the mug substrate. These results contribute to our understanding of the impact of various cleaning methods on DNA recovery at the crime scene and will help inform DNA recovery strategies

Dynamic scaling approach to study time series fluctuations

We propose a new approach for properly analyzing stochastic time series by mapping the dynamics of time series fluctuations onto a suitable nonequilibrium surface-growth problem. In this framework, the fluctuation sampling time interval plays the role of time variable, whereas the physical time is treated as the analog of spatial variable. In this way we found that the fluctuations of many real-world time series satisfy the analog of the Family-Viscek dynamic scaling ansatz. This finding permits to use the powerful tools of kinetic roughening theory to classify, model, and forecast the fluctuations of real-world time series.Comment: 25 pages, 7 figures, 1 tabl

Multifractal Dimensions for Branched Growth

A recently proposed theory for diffusion-limited aggregation (DLA), which models this system as a random branched growth process, is reviewed. Like DLA, this process is stochastic, and ensemble averaging is needed in order to define multifractal dimensions. In an earlier work [T. C. Halsey and M. Leibig, Phys. Rev. A46, 7793 (1992)], annealed average dimensions were computed for this model. In this paper, we compute the quenched average dimensions, which are expected to apply to typical members of the ensemble. We develop a perturbative expansion for the average of the logarithm of the multifractal partition function; the leading and sub-leading divergent terms in this expansion are then resummed to all orders. The result is that in the limit where the number of particles n -> \infty, the quenched and annealed dimensions are {\it identical}; however, the attainment of this limit requires enormous values of n. At smaller, more realistic values of n, the apparent quenched dimensions differ from the annealed dimensions. We interpret these results to mean that while multifractality as an ensemble property of random branched growth (and hence of DLA) is quite robust, it subtly fails for typical members of the ensemble.Comment: 82 pages, 24 included figures in 16 files, 1 included tabl

No self-similar aggregates with sedimentation

Two-dimensional cluster-cluster aggregation is studied when clusters move both diffusively and sediment with a size dependent velocity. Sedimentation breaks the rotational symmetry and the ensuing clusters are not self-similar fractals: the mean cluster width perpendicular to the field direction grows faster than the height. The mean width exhibits power-law scaling with respect to the cluster size, ~ s^{l_x}, l_x = 0.61 +- 0.01, but the mean height does not. The clusters tend to become elongated in the sedimentation direction and the ratio of the single particle sedimentation velocity to single particle diffusivity controls the degree of orientation. These results are obtained using a simulation method, which becomes the more efficient the larger the moving clusters are.Comment: 10 pages, 10 figure

Diffusion-Limited Aggregation Processes with 3-Particle Elementary Reactions

A diffusion-limited aggregation process, in which clusters coalesce by means of 3-particle reaction, A+A+A->A, is investigated. In one dimension we give a heuristic argument that predicts logarithmic corrections to the mean-field asymptotic behavior for the concentration of clusters of mass $m$ at time $t$, $c(m,t)~m^{-1/2}(log(t)/t)^{3/4}$, for $1 << m << \sqrt{t/log(t)}$. The total concentration of clusters, $c(t)$, decays as $c(t)~\sqrt{log(t)/t}$ at $t --> \infty$. We also investigate the problem with a localized steady source of monomers and find that the steady-state concentration $c(r)$ scales as $r^{-1}(log(r))^{1/2}$, $r^{-1}$, and $r^{-1}(log(r))^{-1/2}$, respectively, for the spatial dimension $d$ equal to 1, 2, and 3. The total number of clusters, $N(t)$, grows with time as $(log(t))^{3/2}$, $t^{1/2}$, and $t(log(t))^{-1/2}$ for $d$ = 1, 2, and 3. Furthermore, in three dimensions we obtain an asymptotic solution for the steady state cluster-mass distribution: $c(m,r) \sim r^{-1}(log(r))^{-1}\Phi(z)$, with the scaling function $\Phi(z)=z^{-1/2}\exp(-z)$ and the scaling variable $z ~ m/\sqrt{log(r)}$.Comment: 12 pages, plain Te

Interfaces with a single growth inhomogeneity and anchored boundaries

The dynamics of a one dimensional growth model involving attachment and detachment of particles is studied in the presence of a localized growth inhomogeneity along with anchored boundary conditions. At large times, the latter enforce an equilibrium stationary regime which allows for an exact calculation of roughening exponents. The stochastic evolution is related to a spin Hamiltonian whose spectrum gap embodies the dynamic scaling exponent of late stages. For vanishing gaps the interface can exhibit a slow morphological transition followed by a change of scaling regimes which are studied numerically. Instead, a faceting dynamics arises for gapful situations.Comment: REVTeX, 11 pages, 9 Postscript figure

Nontrivial Polydispersity Exponents in Aggregation Models

We consider the scaling solutions of Smoluchowski's equation of irreversible aggregation, for a non gelling collision kernel. The scaling mass distribution f(s) diverges as s^{-tau} when s->0. tau is non trivial and could, until now, only be computed by numerical simulations. We develop here new general methods to obtain exact bounds and good approximations of $\tau$. For the specific kernel KdD(x,y)=(x^{1/D}+y^{1/D})^d, describing a mean-field model of particles moving in d dimensions and aggregating with conservation of ``mass'' s=R^D (R is the particle radius), perturbative and nonperturbative expansions are derived. For a general kernel, we find exact inequalities for tau and develop a variational approximation which is used to carry out the first systematic study of tau(d,D) for KdD. The agreement is excellent both with the expansions we derived and with existing numerical values. Finally, we discuss a possible application to 2d decaying turbulence.Comment: 16 pages (multicol.sty), 6 eps figures (uses epsfig), Minor corrections. Notations improved, as published in Phys. Rev. E 55, 546

Monitoring birds, reptiles and butterflies in the St Katherine Protectorate, Egypt

Fifty-two bird species were recorded during transect and point count surveys of wadis in the St Katherine Protectorate in the mountainous southern region of the Sinai, Egypt. Two species are new to Egypt: Rock Nuthatch (Sitta neumeyer) and Rock Sparrow (Petronia petronia). There were several other notable species: migrants such as Arabian Warbler (Sylvia leucomelaena) and Upcher’s warbler (Hippolais languida); and residents such as Verreaux’s Eagle (Aquila verreauxi), Hume’s Tawny Owl (Strix butleri) and Striated Scops Owl (Otus brucei).Estimates of bird density and descriptions of each wadi are given. Species diversity of wadis within the Ring dyke geological feature bounding the central mountain plateau was not significantly different from wadis outside. Species composition and numbers of individuals varied according to the distribution of water sources, natural trees and Bedouin gardens especially in fruit. These features appear to be particularly important as staging posts for migrants. Numbers ofsome birds increased around tourist areas. Observations of seven species of reptile and ten species of butterfly including endemics arealso presented. Recorded numbers of all groups depended heavily on the time of day

A pseudo-spectral approach to inverse problems in interface dynamics

An improved scheme for computing coupling parameters of the Kardar-Parisi-Zhang equation from a collection of successive interface profiles, is presented. The approach hinges on a spectral representation of this equation. An appropriate discretization based on a Fourier representation, is discussed as a by-product of the above scheme. Our method is first tested on profiles generated by a one-dimensional Kardar-Parisi-Zhang equation where it is shown to reproduce the input parameters very accurately. When applied to microscopic models of growth, it provides the values of the coupling parameters associated with the corresponding continuum equations. This technique favorably compares with previous methods based on real space schemes.Comment: 12 pages, 9 figures, revtex 3.0 with epsf style, to appear in Phys. Rev.